LIMA, Aug 17 (Reuters) - President Alan Garcia's approval rating has dropped to an all-time low of 22 percent, as higher food prices and a botched earthquake rebuilding effort have frustrated voters, Peru's top polling firm said on Sunday.

Garcia's approval rating fell 4 percentage points from a previous poll in July after being widely criticized in the days leading up to the one-year anniversary on Friday of an 8.0 magnitude earthquake that killed more than 500 people and destroyed at least 37,000 homes.

Garcia, a former leftist who is now a fervent believer in free markets, promised a speedy reconstruction after the temblor, but one year later, many quake victims are jobless and living in one-room shacks. Some are marooned in tent cities.

In the coastal cities south of Lima, where the damage was most severe, only 4 percent of voters gave Garcia positive marks, according to the nationwide poll by Ipsos Apoyo published in the El Comercio newspaper on Sunday.

Hundreds of Peruvian quake victims protested on Friday to complain that millions of dollars in reconstruction funds have never reached them and were diverted or disappeared into inefficient and sometimes corrupt bureaucracies.

In the August poll, 63 percent of voters said their top complaint was higher prices, down from 67 percent in the July poll, while 48 percent said Garcia had failed to fulfill promises, up from 35 percent in July.

Nationwide, many Peruvians say seven years of economic growth has not trickled down to the poor, and the poverty rate is still nearly 40 percent, which analysts say could allow for a left-wing candidate to emerge as a frontrunner in the next presidential election in 2011.

Garcia, who took office in 2006, cannot run for a second consecutive term. (Reporting by Terry Wade; editing by Todd Eastham)

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